Probing color reconnection with underlying event observables at the LHC energies

In this work we study the underlying event (UE) activity as a function of the highest jet transverse momentum ($p_{\rm T}^{\rm jet}$) in terms of the number and summed $p_{\rm T}$ densities of charged particles in the azimuthal region transverse to the $p_{\rm T}^{\rm jet}$ direction. The UE observables normalised to the INEL multiplicity obey an approximate Koba-Nielsen-Olesen (KNO) scaling. Based on PYTHIA~8.2 simulations of $pp$ collisions at LHC energies, we show that the remaining imperfection of the KNO scaling is due to the increasing importance of multiple partonic interactions (MPI) at higher $\sqrt{s}$. Motivated by this, we studied the UE activity considering charged particles within different $p_{\rm T}$ intervals in $pp$ collisions at $\sqrt{s}=7$\,TeV. We demonstrate that the saturations of both number and summed $p_{\rm T}$ densities, which are commonly claimed, are only observed for low-\pt charged particles ($0.5<p_{\rm T}<2$\,GeV/$c$). Moreover, for the $p_{\rm T}$-integrated case ($p_{\rm T}>0.5$\,GeV/$c$) the summed $p_{\rm T}$ density is not sensitive to the variation of color reconnection (CR), however at low-p_{\rm T} it is reduced with increasing CR, whereas an opposite behaviour is found at intermediate-$p_{\rm T}$ ($2<p_{\rm T}<10$\,GeV/$c$). Finally, we show that CR produces flow-like behaviour only in the UE region and the effects are reduced with increasing $p_{\rm T}^{\rm jet}$ due to the hardering of UE. The outcomes encourage the measurement of inclusive and identified charged particle $p_{\rm T}$ spectra (over a wide range of $p_{\rm T}$) associated to UE aimed at better understanding the similarities between $pp$ and heavy-ion data discovered at the LHC.

simulations of pp collisions at LHC energies, we show that the small breaking of the KNO scaling is due to the increasing importance of multiple partonic interactions (MPI) at higher √ s. This in turn makes that with increasing energy, the p T spectra in the UE get harder than in inelastic pp collisions.
Color reconnection (CR) models the interactions among outgoing partons just before the hadronization, therefore it modifies the p T -spectral shape. Motivated by this, we studied the UE activity considering charged particles within different p T intervals in pp collisions at √ s = 7 TeV. Although MPI saturate for p jet T > 10 GeV/c, the UE still increases with increasing p jet T . We demonstrate that the saturation of both number and summed-p T densities,

Introduction
In the context of event generators, one single inelastic (non-diffractive) protonproton (pp) collision can be split into two components: the main hard partonic 3 scattering and the underlying event (UE). The latter includes initial-and finalstate radiation (ISR/FSR), multiple partonic interactions (MPI) and the fragmentation of beam remnants resulting from the hadronization of the partonic 6 constituents that did not participate in any scatter. On top of that, color reconnection (CR) is a microscopic mechanism that describes the interactions that can occur between color fields during the hadronization transition. It is a key 9 ingredient which is needed to explain the increase of the average transverse momentum as a function of charged-particle multiplicity [1] and the multiplicitydependent event shape studies [2]. The importance of the UE relies on the 12 fact that it can shed light in the search for new physics phenomena at hadron colliders [3] or even in the quest for precise Standard Model measurements [4].
The UE observables have been measured in pp collisions in dijet and Drell- 15 Yan processes at CDF at √ s = 1.8 and 1.96 TeV [5,6]. At the start of the LHC most of the existing Monte Carlo models were tuned using Tevatron data. In this sense, early measurements provided by the ATLAS experiment [7] showed 18 clear differences between event generators and data. Latest results have shown an improvement on the description of the UE by the new Monte Carlo tunes [8].
However, we should keep in mind that the modelling of UE is more challenging 21 than traditionally assumed because recent results suggest the unexpected presence of heavy ion-like behavior in pp data [9,10,11,12]. We should therefore go beyond the traditional UE analysis for better understanding the similarities 24 between pp and heavy-ion data.
In order to understand the physics behind high-multiplicity pp collisions, we have performed several studies using PYTHIA 8 [13] event generator. We 27 have found that CR together with MPI can produce radial flow patterns via boosted color strings [14]. The analysis as a function of event multiplicity allows to study events with different amount of MPI, however we have shown 30 that high-multiplicity pp collisions are effected by the so-called fragmentation bias [15,16]. Moreover, for a fixed amount of MPI CR strongly modifies the charged-particle multiplicity, therefore a selection based on multiplicity does not 33 permit the isolation of CR effects in events with the same MPI activity. In this work we propose to exploit the usage of UE in order to increase the sensitivity to events with multiple semi-hard scatterings instead to biased fragmentation 36 of high transverse momentum jets. Similar ideas have been proposed in order to disentangle auto-correlation effects from other physical phenomena by measuring the charged-particle multiplicity in the UE region [17].

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Given that heavy-ion data feature remarkable differences between the particle production associated to bulk (everything outside the jet peaks) and jets [18,19], we have decided to perform an analogous analysis in pp collisions simulated 42 with PYTHIA 8. The advantage is that cutting on the highest charged-particle transverse momentum (p leading T ) or highest jet p T (p jet T ) it is possible to select events with larger (and nearly constant) MPI activity than that associated 45 to inelastic events. This allows to enhance color-reconnection effects on the hadronization.
Specifically, in this paper we study the modification of the traditional UE 48 observables when charged particles within different p T intervals are considered.
We also aim to understand how the underlying-event activity is affected when either p jet T or √ s are varied. The analysis is not restricted to the traditional 51 average quantities, instead we study the p T spectra of unidentified and identified charged particles within UE environments modified with a selection on p jet T . The measurements of the p T spectra sensitive to UE as a function of p jet T are proposed 54 as a tool to probe the QCD Monte Carlo picture using LHC data.
The article is organised as follows: section 2 provides information about the event and particle selection for the simulations, section 3 discusses the energy 57 dependence of the UE in terms of the number and summed-p T densities, section 4 presents the results on how CR affects the UE observables and the p T distribution of identified charged particles, and finally section 5 contains the 60 summary and outlook.

Simulations and analysis
Quantities sensitive to the UE are constructed as follows. The perpendic-63 ular plane to the beam axis is segmented into three regions depending on the azimuthal angular difference (∆φ) relative to the leading object (e.g. jet or charged particle) axis. Unless specified, those particles with π/3 < |∆φ| < 2π/3   [22] results available on HEPData [23], different selections at particle and event levels were implemented: 1. The comparison of simulations with CMS data (pp collisions at √ s = 0.9 78 and 7 TeV) requires a leading jet with transverse momentum larger than 1 GeV/c within the pseudorapidity interval: |η| < 2. Jets are defined using the SISCone algorithm [24] as implemented in FastJet 3.3 [25] with the 81 clustering radius given as R = (∆φ) 2 + (∆η) 2 = 0.5. Furthermore, jets are built using charged particles with p T > 0.5 GeV/c and |η| < 2.5. The UE observables are computed using charged particles within |η| < 2 and 84 p T > 0.5 GeV/c. Notice the η range of particles used to build the jets is larger than that of particles in the UE in order to avoid a kinematic bias. In a previous publication [26], we have shown that within 10% the UE observables as a function of p leading T collapse on √ s-independent curves once they are scaled to the corresponding average charged-particle density (dN ch /dη inelastic ).

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This quantity is obtained for inelastic pp collisions at a given center-of-mass energy. In this paper we want to trace back the origin of the small imperfection of the scaling behavior, i.e. its validity within 10%. Instead of using ATLAS 102 UE data (measured as a function of p leading T ), now we use the CMS data since they are reported for a wide p jet T interval. This allows the study of pp events with exceptional high-p T jets. In order to obtain the charged-particle density, 105 the transverse momentum distributions of charged particles in pp collisions at √ s = 0.9 and 7 TeV [27,28] were integrated for |η| < 2.4 and p T > 0.5 GeV/c. respectively. Therefore, the relative variation (f ) of the average charged-particle density in pp collisions at √ s = 7 TeV with respect to pp collisions at √ s = 0.9 TeV was found to be f = 1.94 ± 0.11.
114 Figure 1 shows the number (left panel) and the summed-p T (right panel) densities as a function of p jet T after scaling by a 1/f factor. Little or no energy dependence is observed after the implementation of the scaling factor. This is 117 what we called "universality of UE" in our previous work where p leading T was used instead [26]. The results are compared with PYTHIA 8 simulations since it reproduces very well many features of LHC data. We observe that the scaling 120 properties hold up to p jet T = 25 GeV/c. Regarding the behavior of data, a steep rise of the underlying activity with increasing p jet T is observed. This fast rise is followed by a change of the slope above p jet T ∼ 10 GeV/c.  Data were obtained from [21,29].
which yields to a saturation of the MPI activity. Different publications state that above 10 GeV/c the UE observables saturate, reaching nearly constant 126 values [22,8,30]. However, we want to stress the fact that both data and PYTHIA 8 still show a rise of the UE activity with increasing p jet T . In the next sections we discuss how color reconnection contributes to that behavior.

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The universality of UE can be interpreted as the approximate Koba-Nielsen-Olesen (KNO) [31] scaling of the particle production associated to the UE. For this reason we studied the energy dependence of the KNO variable: number den-132 sity in the transverse side normalised to the charged-particle density (inelastic pp collisions). This ratio has been studied by ALICE using pp data at √ s = 0.9 and 7 TeV [22]. To obtain the numerator, ALICE fitted a first degree polynomial In order to investigate the features of particle production associated to UE, 153 in particular the excess of particles in UE with respect to inelastic pp collisions, we studied the p T spectra of unidentified charged particles. The CMS collabo-ration has reported such spectra for pp collisions at √ s = 0.9 and 7 TeV. The UE corresponds to events with p jet T > 3 GeV/c within |η| < 2. To study the evolution of the p T -differential particle production with increasing energy, the 7 TeV p T spectrum was normalized to the corresponding one at 0.9 TeV. The 159 results are presented in the right-hand side of Fig. 2. An analogous ratio as a function of p T was obtained using the p T spectra of inelastic pp collisions at the same energies [29]. Within uncertainties, both ratios are consistent up

CR studies using UE observables
We have shown that, with increasing √ s, the p T spectra sensitive to UE get 171 harder than that in inelastic events as a consequence of the √ s dependence of MPI. Since in events with large number of MPI color reconnection modifies the particle production [14], CR effects on UE are expected. In order to quantify parison between data and PYTHIA 8 over a broad p jet T interval. Since we claim an approximate scaling of the particle production associated to UE, we report results only for pp collisions at √ s = 7 TeV. The conclusions should hold for 189 other energies.
Modification of the particle production at low and intermediate p T . Figure 3 shows the number density as a function of p jet T for pp collisions at The corresponding plots for the summed-p T density are shown in Fig. 4.

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Contrary to the number density, this observable presents a steeper rise with increasing p jet T and no color-reconnection effects are visible for the p T -integrated case. However, this does not happen when the summed-p T density is calculated 207 considering low-or intermediated-p T charged particles. Namely, for low-p T particles the summed-p T density shows a saturation for p jet T > 10 GeV/c. Moreover, the summed-p T density decreases with increasing values of rr (the CR 210 effect amounts to 5%). For the intermediate-p T case, the summed-p T density rises with increasing p jet T more or less at the same rate that the p T -integrated case.

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In order to avoid any possible jet effect (at small values of |∆η|) that could bias the previous results, an extra cut on |∆η| was tested. In this sense only particles with |∆η| > 1.6 were selected, but no significant differences were ob-216 served.
In short, the behavior of the number density as a function of p jet T is determined by low-momenta particles while for summed-p T density is determined by  Flow-like effects within a hard UE environment. It has been shown that CR produces flow-like effects that increase with increasing N MPI [14]. This is because the number of strings connecting scattered partons naturally increases with increasing N MPI . CR allows the color fields of the event to be redirected, relative to the case of color-separated MPI, in such a way that the total string length is reduced. This produces a transverse boost to reconnected string pieces, 231 that e.g. provides to heavier hadrons higher p T [32]. It has been shown that in events with enhanced UE activity, relative to inelastic pp collisions, the flow-like effects increase. This has been achieved by selecting highly-spherical 234 events where no jet structure is present [33]. Motivated by the similarity of the event-shape selection results with those for heavy-ion collisions where the proton-to-pion ratio (sensitive to radial flow [34]) is studied for the regions 237 sensitive to bulk production and jet fragmentation, separately. We decided to perform an analogous Monte Carlo analysis but considering the underlying event accompanying a very high-p T jet. The goal of the study is to understand how 240 the p jet T selection affects observables sensitive to radial flow in the UE region. Figure 5 shows the proton-to-pion ratio as a function of the hadron transverse momentum in the underlying-event region for two p jet T bins and for three different 243 values of rr: 0, 1.8 and 10. The left-hand side of Figure 5 shows the results for 30 < p jet T < 40 GeV/c. Going from independent fragmentation (rr = 0) to the largest value of rr, the proton yield is suppressed with respect to the pion one 246 for p T < 2 GeV/c, whereas for intermediate transverse momentum the proton yield is enhanced relative to the pions. This is the mass effect attributed to color reconnection that was previously reported for the inclusive event [14], i.e. 249 without any separation of the soft and hard components. It is worth noting that the size of the bump shown in Fig. 5 is smaller than that seen in the inclusive case [14]. The reduction is understood in terms of the hardness of 252 the underlying event that increases with increasing p jet T . The right-hand side of Fig. 5 shows the results when we move from 30 < p jet T < 40 GeV/c to higher jet transverse momentum (40 < p jet T < 100 GeV/c). Going from low-to high-p jet T 255 values the structure at p T = 3 GeV/c is reduced. Moreover, the results show a smaller dependence on rr indicating that the ratio is more sensitive to the fragmentation of hard partons.

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Finally, in order to show the distinct behavior of the UE with respect to jet fragmentation, Figure 6 presents the proton-to-pion ratio as a function of p T obtained for the towards region (|∆φ| < π/3). In particular, only pions 261 and protons within R < 0.5 are considered. Notice that, opposite to Figures 3   and 4, the ratios in the bottom panels of Figures 5 and 6 are performed relative to rr = 0. The reason is because in the latter case the goal is to quantify the 264 flow-like effect, if any, that is observed when color reconnection is present.
Overall in Figure 6, the ratio is significantly smaller than the corresponding for the underlying-event region. For example, while for the transverse region The effects reported in this paper should be searched in data; the outcome would contribute to the understanding of the unexpected heavy ion-like signals 279 discovered in small systems by LHC experiments [11,12,35].

Conclusion
Motivated by the results of our previous work [26], where we shown that the 282 particle production sensitive to the underlying event (UE observables) exhibited an approximate KNO scaling. In this paper we investigated in more detail the scaling properties using data from three experiments at the LHC, as well as We studied the number density in the transverse side divided by the charged-  particle density in inelastic pp collisions (KNO variable). Both two quantities were calculated considering charged-particles with p T > 0.5 GeV/c. The ratio was found to increase with increasing √ s, the trend was well described by 291 PYTHIA 8. In particular going from pp collisions at √ s = 0.9 to 7 TeV, the ratio increased by 8-10%. In PYTHIA 8 the rate of such an increase with increasing √ s was close to that for multiple partonic interactions. Moreover, 294 using the limited available data we found indications that particle production at intermediate-p T (2 < p T < 10 GeV/c) increased faster in UE than in inelastic events. Whereas at lower p T , such an increase in both UE and inelastic events 297 was the same within uncertainties. This effect could yield the small breaking (10%) of the KNO scaling in the particle production sensitive to UE.
The results above motivated the study of the traditional underlying-event 300 observables considering particles within different p T intervals. We found that color reconnection modifies the p T spectra of unidentified charged particles, producing a variation in the number and summed-p T densities. In short, color 303 reconnection enhanced the particle production at intermediate transverse momenta in regions far from the jet peaks. The modification was mass dependent, e.g. the proton-to-pion ratio as a function of p T in the underlying-event re-306 gion exhibited a flow-like response with the variation of the color reconnection strength. This behavior was very similar to what was observed in the bulk (everything outside the jet peak) region measured in heavy-ion collisions.

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Our paper encourages the measurement of p T spectra of unidentified and identified charged particles in the transverse side. The variation of such p T spectra as a function of center-of-mass energy, p jet T (or p leading T ), and system size 312 would add key information on the origin of the heavy ion-like effects observed in pp collisions.

Acknowledgments
We acknowledge the technical support of Luciano Diaz and Eduardo Murrieta for the maintenance and operation of the computing farm at ICN-UNAM. Support for this work has been received from CONACyT under the Grant No.